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%I #15 Feb 03 2016 17:04:09
%S 0,2,2,6,3,20,4
%N Number of n-vertex simple graphs G_n for which n does not divide the number of labeled copies of G_n.
%C Let G_n be an n-vertex simple graph, with a(G_n) automorphisms. Then l(G_n) = n!/a(G_n) is the number of labeled copies of G_n. So a(n) is the number of G_n for which n does not divide l(G_n).
%C For prime p, a(p) is the number of circulants of order p.
%C The number of circulants of order n is A049287(n).
%D John P. McSorley, Smallest labelled class (and largest automorphism group) of a tree T_{s,t} and good labellings of a graph, preprint, (2016).
%D R. C. Read, R. J. Wilson, An Atlas of Graphs, Oxford Science Publications, Oxford University Press, (1998).
%D James Turner, Point-symmetric graphs with a prime number of points, Journal of Combinatorial Theory, vol. 3 (1967), 136-145.
%e If n=3 then both G_3 = K_3 and its complement have a(G_3) = 6, so l(G_3) = 3!/6 = 1, and so 3 does not divide l(G_3); no other graphs G_3 satisfy this, so a(3)=2.
%Y A000088 minus A266478.
%Y Cf. A049287.
%K nonn,hard,more
%O 1,2
%A _John P. McSorley_, Dec 29 2015
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